A Top-down Approach to Combining Logics

Christoph Benzmüller

Abstract

The mechanization and automation of combination of logics, expressive ontologies and notions of context are prominent current challenge problems. I propose to approach these challenge topics from the perspective of classical higher-order logic. From this perspective these topics are closely related and a common, uniform solution appears in reach.

References

  1. Akman, V. and Surav, M. (1996). Steps toward formalizing context. AI Magazine, 17(3).
  2. Andrews, P. B. (1971). Resolution in Type Theory. Journal of Symbolic Logic, 36(3):414-432.
  3. Andrews, P. B. (1972). General models and extensionality. Journal of Symbolic Logic, 37:395-397.
  4. Andrews, P. B. (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers, second edition.
  5. Baldoni, M. (1998). Normal Multimodal Logics: Automatic Deduction and Logic Programming Extension. PhD thesis, Universita degli studi di Torino.
  6. Benzmüller, C. (1999). Extensional higher-order paramodulation and RUE-resolution. Automated Deduction, CADE-16, Proc., number 1632 in LNCS, pages 399- 413. Springer.
  7. Benzmüller, C. (2002). Comparing approaches to resolution based higher-order theorem proving. Synthese, 133(1- 2):203-235.
  8. Benzmüller, C. (2009). Automating access control logic in simple type theory with LEO-II. Emerging Challenges for Security, Privacy and Trust, SEC 2009, Proc., volume 297 of IFIP, pages 387-398. Springer.
  9. Benzmüller, C. (2011). Combining and automating classical and non-classical logics in classical higher-order logic. Annals of Mathematics and Artificial Intelligence, 62(1-2):103-128.
  10. Benzmüller, C., Brown, C., and Kohlhase, M. (2004). Higher-order semantics and extensionality. Journal of Symbolic Logic, 69(4):1027-1088.
  11. Benzmüller, C., Gabbay, D., Genovese, V., and Rispoli, D. (2012). Embedding and automating conditional logics in classical higher-order logic. Annals of Mathematics and Artificial Intelligence. In Print. DOI 10.1007/s10472-012-9320-z.
  12. Benzmüller, C. and Genovese, V. (2011). Quantified conditional logics are fragments of HOL. Presented at the Int. Conference on Non-classical Modal and Predicate Logics (NCMPL). Available as arXiv:1204.5920v1.
  13. Benzmüller, C. and Paulson, L. (2008). Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II. Festschrift in Honor of Peter B. Andrews on His 70th Birthday. College Publications.
  14. Benzmüller, C. and Paulson, L. C. (2010). Multimodal and intuitionistic logics in simple type theory. The Logic Journal of the IGPL, 18:881-892.
  15. Benzmüller, C. and Paulson, L. C. (2012). Quantified multimodal logics in simple type theory. Logica Universalis. In Print. DOI 10.1007/s11787-012-0052-y.
  16. Benzmüller, C. and Pease, A. (2012). Higher-order aspects and context in SUMO. Journal of Web Semantics, 12- 13:104-117.
  17. Benzmüller, C., Rabe, F., and Sutcliffe, G. (2008). The core TPTP language for classical higher-order logic. Automated Reasoning, IJCAR 2008, Proc., volume 5195 of LNCS, pages 491-506. Springer.
  18. Brown, C. (2007). Automated Reasoning in HigherOrder Logic: Set Comprehension and Extensionality in Church's Type Theory. College Publications.
  19. Buvac, S., Buvac, V., and Mason, I. A. (1995). Metamathematics of contexts. Fundamenta Informaticae, 23(3):263-301.
  20. Church, A. (1940). A formulation of the simple theory of types. Journal of Symbolic Logic, 5:56-68.
  21. Giunchiglia, F. (1993). Contextual reasoning. Epistemologia (Special Issue on Languages and Machines), 16:345-364.
  22. Giunchiglia, F. and Serafini, L. (1994). Multilanguage hierarchical logics or: How we can do without modal logics. Artificial Intelligence, 65(1):29-70.
  23. Guha, R. V. (1991). Context: A Formalization and Some Applications. PhD thesis, Stanford University.
  24. Henkin, L. (1950). Completeness in the theory of types. Journal of Symbolic Logic, 15:81-91.
  25. Hoder, K. and Voronkov, A. (2011). Sine qua non for large theory reasoning. Automated Deduction, CADE-23, Proc., volume 6803 of LNCS, pages 299-314.
  26. Huet, G. (1973). A Complete Mechanization of Type Theory. In Proc. of the 3rd International Joint Conference on Artificial Intelligence , pages 139-146.
  27. Huet, G. (1975). A Unification Algorithm for Typed Lambda-Calculus. Theoretical Computer Science, 1(1):27-57.
  28. Lehmann, J., Varzinczak, I. J., and (eds.), A. B. (2012). Reasoning with context in the semantic web. Web Semantics: Science, Services and Agents on the World Wide Web, 12-13:1-160.
  29. McCarthy, J. (1987). Generality in artificial intelligence. Communications of the ACM, 30(12):1030-1035.
  30. McCarthy, J. (1993). Notes on formalizing context. In Proc. of IJCAI'93, pages 555-562.
  31. Meng, J. and Paulson, L. C. (2009). Lightweight relevance filtering for machine-generated resolution problems. Journal of Applied Logic, 7(1):41-57.
  32. de Paiva, V. (2003). Natural deduction and context as (constructive) modality. In Modeling and Using Context, Proc. of CONTEXT 2003, volume 260 of LNCS, Stanford, CA, USA. Springer.
  33. Ohlbach, H.-J. (1991). Semantics Based Translation Methods for Modal Logics. Journal of Logic and Computation, 1(5):691-746.
  34. Pease, A., editor (2011). Ontology: A Practical Guide. Articulate Software Press, Angwin, CA 94508.
  35. Pease, A., Sutcliffe, G., Siegel, N., and Trac, S. (2010). Large theory reasoning with SUMO at CASC. AI Communications, 23(2-3):137-144.
  36. Pietrzykowski, T. and Jensen, D. (1972). A Complete Mechanization of Omega-order Type Theory. Proc. of the ACM Annual Conf., pages 82-92. ACM Press.
  37. Ramachandran, D., Reagan, P., and Goolsbey, K. (2005). First-orderized ResearchCyc: Expressivity and efficiency in a common-sense ontology. In P., S., editor, Papers from the AAAI Workshop on Contexts and Ontologies: Theory, Practice and Applications, Pittsburgh, Pennsylvania, USA, 2005. Technical Report WS-05-01, AAAI Press, Menlo Park, California.
  38. Segerberg, K. (1973). Two-dimensional modal logic. Journal of Philosophical Logic, 2(1):77-96.
  39. Serafini, L. and Bouquet, P. (2004). Comparing formal theories of context in AI. Artif. Intell., 155:41-67.
  40. Stalnaker, R. (1968). A theory of conditionals. Studies in Logical Theory, American Philosophical Quarterly, Monogr. Series no.2, page 98-112. Blackwell, Oxford.
  41. Sutcliffe, G. (2007). TPTP, TSTP, CASC, etc. Proc. of the 2nd International Computer Science Symposium in Russia, number 4649 in LNCS, pages 7-23. Springer.
  42. Sutcliffe, G. (2009). The TPTP problem library and associated infrastructure. Journal of Automated Reasoning, 43(4):337-362.
  43. Sutcliffe, G. and Benzmüller, C. (2010). Automated reasoning in higher-order logic using the TPTP THF infrastructure. Journal of Formalized Reasoning, 3(1):1-27.
  44. Thomason, R. H. (1984). Combinations of tense and modality. Handbook of Philosophical Logic, Vol. 2: Extensions of Classical Logic, pages 135-165. D. Reidel.
  45. Woods, J. and Gabbay, D. M., editors (since 2004). Handbook of the History of Logic, volumes 1-8. Elsevier.
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Paper Citation


in Harvard Style

Benzmüller C. (2013). A Top-down Approach to Combining Logics . In Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8565-39-6, pages 346-351. DOI: 10.5220/0004324803460351


in Bibtex Style

@conference{icaart13,
author={Christoph Benzmüller},
title={A Top-down Approach to Combining Logics},
booktitle={Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2013},
pages={346-351},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004324803460351},
isbn={978-989-8565-39-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - A Top-down Approach to Combining Logics
SN - 978-989-8565-39-6
AU - Benzmüller C.
PY - 2013
SP - 346
EP - 351
DO - 10.5220/0004324803460351